Miniature heat exchangers are used to provide higher cooling capacity for new technologies. This means a reduction in their size and cost but the identical power. The paper presents the method for determination of boiling heat transfer coefficient for a rectangular minichannel of 0.1 mm depth, 40 mm width and 360 mm length with asymmetric heating. Experimental research has focused on the transition from single phase forced convection to nucleate boiling, i.e., the zone of boiling incipience. The ‘boiling front’ location has been determined from the temperature distribution of the heated wall obtained from liquid crystal thermography. The experiment has been carried out with R-123, mass flux 220 kg/(m2s), pressure at the channel inlet 340 kPa. Local values of heat transfer coefficient were calculated on the basis of empirical data from the experiment following the solution of the two-dimensional inverse heat transfer problem. This problem has been solved with the use of the finite element method in combination with Trefftz functions. Temperature approximates (linear combinations of Trefftz functions) strictly fulfill the governing equations. In presented method the inverse problem is solved in the same way as the direct problem. The results confirmed that considerable heat transfer enhancement takes place at boiling incipience in the minichannel flow boiling. Moreover, under subcooling boiling, local heat coefficients exhibit relatively low values.